Chapter 1: Q11-30E (page 1)

A vertical, solid steel post 25 cm in diameter and 2.50 m long is required to support a load of 8000 Kg. You can ignore the weight of the post. What are (a) the stress in the post; (b) the strain in the post; and (c) the change in the post’s length when the load is applied?

Short Answer

Expert verified

$(a) - 1.60 \times 10^{6} P a (b) - 8 \times 10^{- 6} (c) - 2.0 \times 10^{- 5} m$

Step by step solution

Given information

Length I₀= 2.50m, diameter d = 2.5x10^-2m, Load m = 8000kg

Concept/Formula used

$Y = \frac{l_{0} F}{AΔl}$

Where, Y is Young’s modulus, I₀ is length of muscle, F is muscle force, A is cross-sectional area and $∆ l$ is elongation.

Cross –sectional area of the post

$\begin{array}{rcl} A & = & π (\frac{d^{2}}{4}) \\ = & π (\frac{{(2.50 \times 10^{- 2} m)}^{2}}{4}) \\ = & 0.05 m^{2} \end{array}$

Force application on the post

$F = m g = (8000 k g) (9.80 m / s^{2}) = 7.84 \times 10^{4} N Y o u n g ’ s M o d u l u s f o r s t e e l i s Y = 2.0 \times 10^{11} P a$

Stress in the post

(a)

$s t r e s s = \frac{F}{A} = - \frac{7.84 \times 10^{4} N}{0.05 m^{2}} = - 1.60 \times 10^{6} P a$

Note: negative sign shows that the stress is compressive.

Strain in the post

(b)

$\begin{array}{rcl} s t r a i n & = & \frac{s t r e s s}{Y} \\ = & - \frac{1.60 \times 10^{6} P a}{2 \times 10^{11} P a} \\ = & - 8 \times 10^{- 6} \end{array}$

Note: negative sign shows that the length decreases.

Change in the post length

(C)

$\begin{array}{rcl} Δ l & = & l_{0} (s t r a i n) \\ = & (2.5 m) (- 8 \times 10^{- 6}) \\ = & - 2.0 \times 10^{- 5} m \end{array}$

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A vertical, solid steel post 25 cm in diameter and 2.50 m long is required to support a load of 8000 Kg. You can ignore the weight of the post. What are (a) the stress in the post; (b) the strain in the post; and (c) the change in the post’s length when the load is applied?

Short Answer

Step by step solution

Given information

Concept/Formula used

Cross –sectional area of the post

Force application on the post

Stress in the post

Strain in the post

Change in the post length

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